This paper investigates the problem of dynamic multiuser subchannel allocation in the downlink OFDM systems. In traditional TDMA or FDMA systems, resource allocation for each user is non-adaptively fixed. Since the subchannel allocations among the users are not optimized, a group of users is likely to suffer from poor channel gains resulting from large path loss and random fading. To resolve this problem a low-complexity adaptive subchannel allocation algorithm is proposed in this paper. By adaptively assigning frequency subchannels, n take advantage of channel diversity among users in different locations, which is called Multiuser diversity. The capacity of MU-OFDM is maximized when each subchannel is assigned to the user with the best channel-tonoise ratio for that subchannel. However, fairness among the users cannot generally be achieved with such a scheme. In this paper, a set of proportional fairness constraints is imposed to assure that each user achieve a required data rate, that ensures quality of service. In the proposed algorithm, subchannel allocation is performed by assuming an equal power distribution.